Mathematics - 2012-09-03 (page 2 of 2)

hhh

8:00 PM

@JayeshBadwaik Can you recommend me book or exercises?

Peter Tamaroff

@hhh *me

hhh

@PeterTamaroff sure, fixed :)

Jayesh Badwaik

@hhh I am looking at your book right now. Considering it is based on halliday resnick, I think its exercises are good enough. Will just see and let you know though.

Jonas Teuwen

@JohnSenior A document from my beard.

Jayesh Badwaik

In case you want another book you can choose any one of electrodynamics griffith, electromagnetics nathan ida, field and wave electromagnetics david cheng. titles are not exactly these but I guess the books are popular enough to show up on google.

Jonas Teuwen

8:05 PM

You burned me and left me badly disfigured! laughed the Indian boy.

Jayesh Badwaik

Have you guys heard about John Rainwater?

at.yorku.ca/t/o/p/d/47.htm

Got the idea by looking at JT and anonymous.

John Senior

@JonasTeuwen wonderful!

Jonas Teuwen

Ah!

Jayesh Badwaik

@JonasTeuwen That was like Lewis Caroll giving the Queen the next book he published after "Alice in Wonderland" :P

Jonas Teuwen

You and your books...

Jayesh Badwaik

8:10 PM

Hahaha. Okay I will shut up. More integrals, less books!

John Senior

@JayeshBadwaik less integrals - more zeta functions ...

there are so many of those beasts!

Michael Greinecker

@Jonas I'm looking at the Dleft troll work. I don't get what you mean when you write that $[0,1]^[0,1]$ endowed with the product topology "is the space of all continuous mappings on [0, 1]." The space contains all mappings $f:[0,1]\to [0,1]$, not just continuous ones.

Jonas Teuwen

Oh, I thought that made them all continuous.

I thought it was the same as the weak topology here.

Jayesh Badwaik

Right now I am on this problem. Show that
\begin{equation}
\int\limits_{0}^{\infty} x^{-x} \mathrm{d}x = \sum\limits_{n=1}^{\infty} n^{-n}
\end{equation}

I can do such things by writing this out as a riemann sum and then evaluating. However, is there some other method which we can apply here? Any other methods of converting integrals to sums?

hhh

@JayeshBadwaik Thank you will check them.

Peter Tamaroff

8:25 PM

How can I make W|A plot some 3D points?

Jonas Teuwen

Slice it.

And then combine!

Peter Tamaroff

@JonasTeuwen Dude.

Jonas Teuwen

8:42 PM

@MichaelGreinecker I wanted to take a space with large cardinality as per your suggestion.

Peter Tamaroff

Is there anyone here who can help me with some vector algebra?

John Senior

@PeterTamaroff I am sure there are - I might even remember a bit myself

John Junior

Slice and combine ;-D

Jayesh Badwaik

@JohnJunior Do not take offense man. It is a line from a song by beatles.

Peter Tamaroff

@JohnSenior OK.

The task is as follows.

We're working on $\mathbb R^3$

John Senior

8:53 PM

@PeterTamaroff I'm happy so far ...

Peter Tamaroff

We got $\Pi:2x-y+2z=4$, $P=(2,2,2)$ and $Q=(1,0,1)$

John Senior

@PeterTamaroff OK

Peter Tamaroff

We need to find a plane $\Pi'$ such that $Q,P\in \Pi'$ and $\Pi'$ contains another point $R$ from $\Pi$ such that $d(P,R)=d(P,\Pi)$.

I have done some work already.

Namely, we have that $d(P,\Pi)=2/3$

Also, say $R=(x_0,y_0,z_0)$

Then we need $(x_0-2)^2+(y_0-2)^2+(z_0-2)^2=4/9$

Now I will plug in $\Pi$ to get things going =P

Jayesh Badwaik

Wouldn't $R$ be the point where the perpendicular from P intersects the $\Pi$ plane?

John Senior

@JayeshBadwaik pretty sure that will be true

Peter Tamaroff

8:58 PM

@JayeshBadwaik I need that $2x_0-y_0+2z_0=4$, too.

Jayesh Badwaik

Then you already have $R$, since $d(P,R)=d(P,\Pi)$. You just have to take the line passing through $P$ and with the direction $(2,-1,2)$ and then find out the point at that distance. So now your 3-variable problem is now one variable (parameter of the line).

Peter Tamaroff

@JayeshBadwaik Let me think.

John Senior

@JayeshBadwaik yep

Peter Tamaroff

@JayeshBadwaik $(2,-1,2)$ is the normal vector.

Jayesh Badwaik

@PeterTamaroff yup

Peter Tamaroff

9:03 PM

@JayeshBadwaik I'm trying to find a plane that contains two points from another plane $Q$ and $R$, and another $P$-

And with some distance contraints.

@JayeshBadwaik It is true that $d(P,\Pi)=2/3$ right?

Jayesh Badwaik

If you can find the three points. Then the normal vector of the other plane will simply be $\bar{PQ} \times \bar{PR}$

Peter Tamaroff

@JayeshBadwaik Yes, I use that often

@JayeshBadwaik Since $Q\in \Pi$ I can calculate the distance as $|(Q-P)\cdot N|/||N||$, yes?

Jayesh Badwaik

Yes

Jonas Teuwen

@JohnSenior Serious issue here.

No beer!

@JayeshBadwaik What is wrong with you? 8-). Just pick Jackson, start working (with mouth shut).

robjohn

@JayeshBadwaik I have done that integral by writing $x=e^{-u}$ and then writing $x^{-x}=\sum\limits_{k=0}^\infty\frac{e^{-ku}u^k}{k!}$

John Senior

9:07 PM

@JonasTeuwen Sh*t!!! - is there an emergency helpline you can ring?

Jonas Teuwen

Rob, the master of Syntax.

@JohnSenior I think they will blacklist my number.

You mean like 0900 - BEER-NOW ?

Peter Tamaroff

@JayeshBadwaik OK, so now how do I work out what $R$ must be?

$R$ is on a circle around $P$

Jayesh Badwaik

@robjohn Oh boy. That is nice :-)

John Senior

@JonasTeuwen yep - we have something similar here in Warrington UK

Jonas Teuwen

@JohnSenior Do they have more beer than just one kind...?

robjohn

9:09 PM

@JayeshBadwaik Then you finish off using the $\Gamma$ function to integrate each term.

Jonas Teuwen

If I have a beard I will be John Junior. My father is John Senior.

Jayesh Badwaik

@robjohn Yup. :-)

@PeterTamaroff Why is it a circle? P is not in $\Pi$ and the distance to the plane is the shortest distance, surely it must be attained at a single point?

John Junior

I would be glad to have you as my brother :)

Peter Tamaroff

@JayeshBadwaik I mean, I have just fixed one part of $R$

Jayesh Badwaik

since $R$ is in the plane.

John Senior

9:10 PM

@JonasTeuwen here

Peter Tamaroff

the one that asks for $d(P,R)=2/3$

Now I need to finish.

Jonas Teuwen

Pretty good song.

@JohnSenior Pretty cool.

Jayesh Badwaik

@PeterTamaroff The sphere of the radius 2/3 around P intersects the plane $\Pi$ at only one point (touches rather)

Peter Tamaroff

@JonasTeuwen The bird is greater than or equal to the word.

2

John Senior

@JonasTeuwen I think I found out what is wrong with my Linux desktop

Peter Tamaroff

9:13 PM

@JayeshBadwaik But I'm being ask that $P\in \Pi'$.

Jonas Teuwen

@JohnSenior It does not run my LFS?

Peter Tamaroff

@JayeshBadwaik Let me rewrite the problem.,

Jayesh Badwaik

@PeterTamaroff yup, that would be good.

John Senior

@JonasTeuwen I have the OS installed on an SSD, and it seems to have developed errors - I have files that I can't delete :(

Peter Tamaroff

@JayeshBadwaik Given $\Pi :2x-y+2z=4$ and $P=(2,2,2)$, $Q=(1,0,1)$, determine a plane $\Pi'$ that contains $P$, $Q$ and a point $R$ of $\Pi$ such that $d(P,R)=d(P,\Pi)$

robjohn

9:14 PM

@JohnSenior Somehow a bottle of wine sounds so much more refined than a crate of beer. :-)

Peter Tamaroff

►

John Senior

@robjohn I agree - but the area of North West UK where I live is not well-known for being refined :)))

many of the guys round here can tie their shoelaces without bending down ...

Peter Tamaroff

@JayeshBadwaik I could visualize it.

Jayesh Badwaik

@PeterTamaroff Yup. So you have a point $P$ outside a plane $\Pi$. Now you have the shortest distance from $P$ to $\Pi$ (which will be the perpendicular distance). Now, another point on $\Pi$ namely $R$ is at the same distance from $P$. surely $R$ must be the point where the perpendicular from $P$ intersects the plane? Followed till here?

Peter Tamaroff

@JayeshBadwaik OK, yes.

Jayesh Badwaik

9:20 PM

So, now your $R$ lies on a line Which can be given as $\bar{X} = \bar{P} + t\bar{N}$, agreed? Where $N$ is the normal vector of the plane.

$t \in R$

Peter Tamaroff

@JayeshBadwaik OK, so I need to find that new $N$, right?

Jayesh Badwaik

No.

Peter Tamaroff

@JayeshBadwaik But that also depends on $R$!

Jayesh Badwaik

You need to find the appropriate $t$.

Peter Tamaroff

@JayeshBadwaik So that $||t N||=2/3$?

Jayesh Badwaik

9:21 PM

Yup

Jonas Teuwen

@JohnSenior Oh, reinstall OS.

@JohnSenior Does the linux kernel fully support your SSD?

The probability brother is here!

Too little Gaussians in my work.

Or too much.

I am trying to figure out what the interesting class of differential operators is where their invariant measure is some nice probability measure such that the eigenfunctions are of (pseudo)binomial type.

Peter Tamaroff

@JayeshBadwaik But what is $N$ then???

If I haven't found $\Pi '$ yet.

Jayesh Badwaik

@PeterTamaroff Normal vector of the plane $(2,-1,2)$

N is the normal vector of $\Pi$

Jonas Teuwen

But maybe Ornstein-Uhlenbeck and Gaussian is enough when I have these cool SDE transformation thingies.

John Senior

@JonasTeuwen I was planning to reinstall this evening, but it is a bit late now

Jonas Teuwen

9:25 PM

Puuurfect.

Only takes like half an hour or so?

John Senior

@JonasTeuwen I thought it did - but I think I will reinstall on a standard drive (I have lots of them lying around)

Jonas Teuwen

@JohnSenior Yeah, no need SSD.

Jayesh Badwaik

@JohnSenior Good. I think even now SSD's are to be preferred for only read-only operations. Even now they have only like 1 million write cycles limit.

John Senior

But I need a version of Linux which doesn't take all my time to keep it updated - but is also stable (unlike Ubuntu / Mint / etc)

Jonas Teuwen

My whole system fits in the memory.

Peter Tamaroff

9:26 PM

@JayeshBadwaik I can't get it.

Jonas Teuwen

@JayeshBadwaik Per cell. Do you know how bloody many cells there are? RANDOMIZE.

@JohnSenior No Bullshit Linux. Made by me.

Also, Arch.

The good thing about mine is that I remove all the Linux bits.

John Senior

@JonasTeuwen Arch sounds like fun - how complex to install?

Jonas Teuwen

I like the Plan9 and BSD things better.

John Senior

@JonasTeuwen LOL

Jonas Teuwen

@JohnSenior If medium-level of knowledge then not so hard.

@JohnSenior There is a very good Wiki.

Peter Tamaroff

9:27 PM

@JayeshBadwaik OH; SHIT

Jayesh Badwaik

@JonasTeuwen Yeah, but only in recent version do they have proper reuse things where they will not write unless necessary. If your hard drive is around 2 years older, then it doesn't.

@PeterTamaroff Exactly. :-) :D

Peter Tamaroff

$R$ is just $P$ projected orthogonally onto the plane¿

user19161

@JohnSenior Debian, full stop.

John Senior

@JonasTeuwen will give Arch a try tomorrow :)

Jayesh Badwaik

@PeterTamaroff If you want to say that, yes you are correct. :-)

@JohnSenior Arch now uses installscripts to install.

user19161

9:29 PM

@johnjunior I see names are getting complicated in here.

Jonas Teuwen

@JayeshBadwaik Good.

Jayesh Badwaik

@JonasTeuwen They threw away the aif after it was unmaintained for too long.

user19161

I think XFCE is very good, but it still uses several GNOME components at least in Xubuntu, so I will stick to GNOME.

user19161

Also, Ubuntu GNOME shell spin will be out next month as an official derivative.

Peter Tamaroff

@JayeshBadwaik S I need to find $\lambda$ such taht $|\lambda|\cdot ||N||=2/3$?

user19161

9:32 PM

However it seems that Firefox and LibreOffice won't be installed by default in the spin.

Jayesh Badwaik

@PeterTamaroff Yup.

@WillHunting I haven't opened LibreOffice for almost atleast. six months now

user19161

@JayeshBadwaik LibreOffice is the only replacement for Microsoft Office. If it goes down we are all finished.

Jayesh Badwaik

@WillHunting It won't go down. I am saying that I don't actually use it. currently that is. And it is not on the default, you can always install it yourself.

user19161

There will be a GNOME OS and even a Firefox OS in a few years.

John Senior

@WillHunting and there is the lightweight JoliOS

user19161

9:36 PM

@JohnSenior Do you like it? Never heard of.

John Senior

@WillHunting I've used it - but don't really like it - but it can be useful

probably called Joli cloud now

Jayesh Badwaik

@JonasTeuwen You use a desktop? (as opposed to a laptop)?

user19161

It is sad Ubuntu chose Unity over GNOME shell. Otherwise it could be the best OS instead of Debian.

Jonas Teuwen

@JayeshBadwaik I use desktop, tablet and laptop?

Depends where I am.

Jayesh Badwaik

@JonasTeuwen I meant for your LFS.

user19161

9:39 PM

GNOME is radical but organized. Unity seems a disorganized mess to me.

Jonas Teuwen

@JayeshBadwaik Oh, desktop.

@JayeshBadwaik When you have a laptop you usually want to work on it and don't really want to have that things break when having to give a talk.

user19161

@JonasTeuwen You are one of the cool kids.

Jonas Teuwen

Why.

I don't want to be part of the cool kids. They are often even more retarded than I am.

4

user19161

People with tablets are cool kids.

John Senior

gotta go - back later folks

user19161

9:40 PM

People with tables are hot kids.

Jayesh Badwaik

@JonasTeuwen Yup. I tried installing LFS on my laptop though and it was giving weird hardware errors, so I am now on tried and tested Arch and don't want to mess with it currently. Scavenging for desktops currently.
@JohnSenior Later.

user19161

@JohnSenior Bye.

John Senior

bye folks

Kannappan Sampath

Hi @Americo.

Jayesh Badwaik

@WillHunting itwire.com/business-it-news/open-source/…

user19161

9:49 PM

@JayeshBadwaik Rather dramatic. But I think GNOME shell is the desktop for the future, together with Windows 8!

Jayesh Badwaik

@WillHunting I like the idea of the search/predict based models for navigation. I dislike the idea of the complexity (ugliness rather) of the underlying SQL/similar software.

user19161

@JayeshBadwaik I like one desktop for desktops and phones. GNOME is that desktop, not Unity.

Kannappan Sampath

Dead.

Jonas Teuwen

@JayeshBadwaik What. I just mean take kernel and download your own tools.

Jayesh Badwaik

@JonasTeuwen NVIDIA Graphics Card. This was around a year and a half ago and nouveau was not good enough. I did not want any direct binary driver, which would break my X at every upgrade.

Jonas Teuwen

10:00 PM

Oh, I have intel graphics.

Jayesh Badwaik

Also my wifi is broadcomm, not exactly linux friendly.

Well, I will be going now. See you all later.

Peter Tamaroff

@JayeshBadwaik Dude, apparently the plane uis $\Pi':x=z$

hhh

10:17 PM

about a book, 34.13 -equation -- really $\frac{E}{B}=c$ where $c$ is the speed of light or some other constant?

http://200.105.152.242/olimpiada/file.php/1/LIBROS_OLIMPIADAS/FISICA%20SERWAY/34-ElectromagneticWaves.pdf

I found something about antennas :)

(it does not show how to deduce the direction with Maxwell -equations, just state things)

hhh

10:45 PM

@JayeshBadwaik Cannot find the books, have to go library :(

Gustavo Bandeira

11:03 PM

Very few people realize the enormous bulk of contemporay mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known. The languanges could, I imagine, be learnt at a lifetime; mathematics certainly could not. Nor is the subject static. Every year new discoveries are published. In 1951 merely to print brief summaries of a year's mathematical publications required nearly 900 pages of print. In january alone, the summaries had to deal with 451 new books and articles. The publications here mentioned dealt with new topics; the…

4

hhh

@GustavoBandeira Thank you for sharing, good quote.

Gustavo Bandeira

@hhh Yep. =)

hhh

@JayeshBadwaik I could only find solution manual, veethaadiyani.blog.uns.ac.id/files/2011/01/…

(I think I will give up this search, just contacted my teacher about the direction -- asking for clarification what he meant with the $\hat k$ and $\hat j$. For me, it looked arbitrarily chosen but @JayeshBadwaik apparently claimed that they could be deduced from Maxwell equations)

Sov gott!

Hey!

Now I know it.

Q1. $\bar E = E \cos(a\bar x+ b\bar y)$ is a planar wave in $x-y$ -axis, right?
Q2. $\bar E = E \cos(\bar r \cdot \bar h)$ is a planar wave in the direction of $\bar h$, right?
Q3. $\bar E = E \cos(\bar r \cdot \bar h)+E\sin(a\bar x +b\bar y)$ is some combination of a planar waves, right?

Q4. $U(\bar r, t) = A_0 e^{i \left( \bar k \cdot \bar r - wt + \phi \right)}$ and this is just a combination of planar waves, right? You can break this up to trigonometric functions each of which are planar waves -- so the sum of planar waves is ???, is it a planar wave?

Moved the questions to my chat with unsolved problems here.

...I wish universities used Stackexchange :P

Rachel

11:32 PM

Hey, does anyone here know anything about math research related to natural language, specifically semantics?

hhh

Q0904_5: Is the some of planar waves a planar wave?

Gustavo Bandeira

@Rachel Let me check something.

hhh

A0904_5: Suppose $\bar A=\cos(\bar x +wt)$ and $\bar B =\sin(\bar y +\bar z +wt)$ where $t$ is time. Now their sum $\bar A + \bar B$ is moving in the 3D -space $xyz$ over time, right?

Rachel

I don't have a specific question about a problem, by the bye. I am trying to find people and places for grad school.

hhh

Hey, this is totally trivial issue :D

Gustavo Bandeira

11:36 PM

@Rachel springer.com/computer/theoretical+computer+science/book/…

@Rachel I guess this book may deal with what you're searching for.

Rachel

@GustavoBandeira: yes, it might be interesting. But I am more interested in the structure of natural language, or a structure that can do the same things.

Gustavo Bandeira

@Rachel I guess this is one of the points of the book I mentioned, look here.

people.csail.mit.edu/bjuba/papers/usc-1.pdf

Rachel

@Gustavo: Yes, it's interesting. MIT is one place on my list currently.

Gustavo Bandeira

@Rachel Yep. In your case, I guess it's a must

@Rachel udel.edu/~heinz/classes/2010/4-651/MSL-120909.pdf

I've found this.

I just don't know if it's going to be useful.

Rachel

I am familiar with the book they mention (Patree et al. 1990). I believe these people are at Stanford.